Higher localised A-hat genera for proper actions and positive scalar curvature

Hao Guo,   (University of Adelaide)

10:00-11:00, November 9, 2021   Tencent Meeting 299 106 237


I will report on recent joint work with V. Mathai, in which we formulate new topological obstructions to invariant metrics of positive scalar curvature that take into account the cohomology of the classifying space for proper actions. This leads to a natural generalisation of Gromov-Lawson's notion of higher A-hat genera to the setting of proper actions by groups with torsion, and it is conjectured that these invariants are obstructions to invariant positive scalar curvature. We verify this when the cohomology class is generated by elements of degree at most 2, under suitable assumptions, via index theory. Time permitting, I will also mention some obstructions in the non-cocompact setting, again coming from indices of projectively invariant Dirac operators.

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